Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

Determination of Surface Functional Groups in Lignocellulosic Materials by Chemical Derivatization and ESCA Analysis

Simple and convenient methods for determining surface chemical composition of lignocellulosic materials are described. The methods are based on vapor phase fluorine surface derivatization with either trifluoro acetic anhydride (TFAA), tri-fluoro ethanol (TFE) or pentafluorophenyl hydrazine (PFPH) and subsequent Electron Spectroscopy for Chemical Analysis (ESCA). Model cellulosic surfaces with well defined functionalities were used to optimize the derivatization reaction conditions. Detection and accessibility of surface hydroxyl functional groups were investigated in cotton and regenerated cellulose as models. Carboxymethyl cellulose (CMC) was used as a model surface for detection and quantification of carboxylic acid groups. Theoretical conversion curves for derivatization reactions were calculated and used to evaluate the extent of the reactions on the model surfaces. It was found that the conversion was higher for the regenerated cellulose and CMC than for cotton. The protocols developed using the model surfaces were applied to a case study on wood fibers with different degrees of complexity, namely dissolving and chemithermomechanical (CTMP) pulp. Untreated and oxygen-plasma modified pulps were compared with respect to the surface composition of functional groups. According to the derivatization reactions, functionalities containing oxygen were significantly increased on the plasma-treated samples. The effect of the treatment was found to be dependent on the type of pulp. Fluorine derivatization is shown to be an unambiguous method for clear assessment of the chemical functionalities of cellulosic surfaces.     

On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Alloy formation in mechanically activated mixtures

The physical mixtures of hydroxocarbonates of Cu and Ni with aluminium were activated using a laboratory planetary mill. The chemical reactions and alloy formations as the effects of grinding were followed by the phase analysis of solid products based on the thermogravimetry and X-ray diffractometry. Experimental evidence indicates that the nature of reactions and products of mechanical activation was dependent on the amount of aluminium and time of grinding. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mixing mechanisms of vortex ring formed by gravity slumping motion

 This paper is concerned with an experimental investigation of the mixing inside the vortex ring formed by the gravity slumping motion of a dense cloud in a less dense atmosphere. The dynamics of the spreading and instantaneous structures of the turbulent flow were examined by visualization, single and multi-point measurements of velocity and concentration for two heavy gases, carbondioxide (CO₂) and dichlorodifluoromethane (CCl₂F₂), in a configuration in that heavy gas, initially trapped in a reservoir, was released with the rise of a shutter into calm air of a sector-shaped dispersion channel. Visualization of the cloud as a whole showed a spreading motion in which an advancing frontal structure was followed by a stratified flow with a layer of dense fluid of higher velocities near the wall and, on top of it, a layer of dilute fluid whose concentration is controlled by the mixing mechanisms within the head. During the course of spreading, there was always a phase in which the head attained to a constant speed of advance, which occurred as 0.13 m/s for CO₂ and 0.48 m/s for CCl₂F₂. It was interesting to observe for CO₂ that the phase of constant speed took place in between two acceleration phases; the former was due to the initial slumping of the cloud at the exit of the reservoir, and the latter was attributed to the collapse of the head on the transition to the passive dispersion phase. Instantaneous two-dimensional velocity field, measured with particle image velocimeter (PIV), showed that the cloud overran the ambient air which caused the approaching dense fluid deflected away from the wall with significant vertical velocities and downstream-moving separation, and the air trapped under the head resulted in the density inversion which introduced further intricacy to the turbulent structure of the head. Instabilities at the upper free shear layer due to density and velocity discontinuity rolled into periodic array of vortices which engulfed a considerable amount of air as they were convected backwards over the head, but the incorporation of heavy and light fluids was completed with the appearance of microscales after the collapse on the stratified layer. Analyses of the cloud head at different downstream locations also revealed that its size remained unchanged when the speed of advance was constant, allowing the rate of change of the cloud volume being modeled with the rate of spreading. Contours of concentration obtained from digitized PIV pictures confirmed the kinematic features of the mixing revealed by the velocity field and that the concentration values within the large structures were higher than those at the upper part of the stratified layer. Motivated by the experimental observations, a semi-empirical analysis was presented to describe the results and based on local values of the Richardson and Reynolds numbers. Received: 4 October 1995 / Accepted: 4 July 1996     

Interpolation of Bilinear Operators Between Quasi-Banach Spaces

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-Lozanovsky spaces, and Lorentz-Zygmund spaces are presented. The author is supported by the National Science Foundation under grant DMS 0099881. The author is supported by KBN Grant 1 P03A 013 26.     

Solubility of carbon dioxide in aqueous solutions of sodium chloride: Experimental results and correlation

The solubility of carbon dioxide in aqueous solutions of sodium chloride was measured in the temperature range from 40 to 160°C, up to 6 mol-kg salt solutions and total pressures up to 10 MPa. Pitzer's⁽¹⁾ equations as well as the Chen and Evans⁽²⁾ model were used to correlate the new data. Results are reported and compared to literature data and correlations.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.